Figure 1.
Optimal solutions in the first example
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April
2017, 13(2): 825-834.
doi: 10.3934/jimo.2016048
Robust design of sensor fusion problem in discrete time
| 1. | LinJiang Middle School, KaiZhou District, Chongqing, China |
| 2. | College of Mathematical Sciences, Chongqing Normal University, Chongqing, China |
In this paper, we consider a robust sensor scheduling problem which estimates the state of an uncertain process based on measurements obtained by a given set of noisy sensors, where the measurements of sensors are subject to external interference uncertainties. We formulate this problem into a minimax optimal control problem, which is equivalent to a semi-infinite programming problem with a dynamic system. A discretization method is used to solve this problem, where the computation is very large scale in general. We propose an approximation method to reduce the computational complexity. For illustration, two numerical examples are solved.
Keywords:
Robust sensor fusion design,
semi-infinite programming.
Mathematics Subject Classification:
Primary: 49M37; Secondary: 90C34.
Citation:
Xiao Lan Zhu, Zhi Guo Feng, Jian Wen Peng. Robust design of sensor fusion problem in discrete time. Journal of Industrial and Management Optimization,
2017, 13
(2)
: 825-834.
doi: 10.3934/jimo.2016048
![]()
References:
| [1] |
T. Abburi and S. Narasimhan,
Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory, IEEE Transactions on Automatic Control, 59 (2014), 2978-2983.
doi: 10.1109/TAC.2014.2351692. |
| [2] |
Z. L. Deng, Y. Gao, L. Mao, Y. Li and G. Hao,
New approach to information fusion steady-state Kalman filtering, Automatica, 41 (2005), 1695-1707.
doi: 10.1016/j.automatica.2005.04.020. |
| [3] |
Z. G. Feng, K. L. Teo and Y. Zhao,
Branch and bound method for sensor scheduling in discrete time, Journal of Industrial and Management Optimization, 1 (2005), 499-512.
doi: 10.3934/jimo.2005.1.499. |
| [4] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for Kalman filtering, Discrete and ContinuousDynamical Systems, 14 (2006), 483-503.
|
| [5] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for discrete Kalman filtering, Dynamic Systems and Applications, 16 (2007), 393-406.
|
| [6] |
Z. G. Feng, K. L. Teo and V. Rehbock,
Hybrid method for a general optimal sensor scheduling problem in discrete time, Automatica, 44 (2008), 1295-1303.
doi: 10.1016/j.automatica.2007.09.024. |
| [7] |
F. N. Grigor'ev and N. A. Kuznetsov,
Control of the observation process in continuous systems, Problems of Control and Information Theory, 6 (1977), 181-201.
|
| [8] |
F. N. Grigor'ev,
About the control of information processing in discrete automatic systems, Automation and Remote Control, 43 (1982).
|
| [9] |
H. Kushner,
On the optimum timing of observations for linear control systems with unknown initial state, IEEE Transactions on Automatic Control, 9 (1964), 144-150.
|
| [10] |
H. W. J. Lee, K. L. Teo and L. S. Jennings,
Control parametrization enhancing techniques for optimal discrete-valued control problems, Automatica, 35 (1999), 1401-1407.
doi: 10.1016/S0005-1098(99)00050-3. |
| [11] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim,
Sensor scheduling in continuous time, Automatica, 37 (2001), 2017-2023.
doi: 10.1016/S0005-1098(01)00159-5. |
| [12] |
Y. Li, L. W. Krakow, E. K. Chong and K. N. Groom,
Approximate stochastic dynamic programming for sensor scheduling to track multiple targets, Digital Signal Processing, 19 (2009), 978-989.
doi: 10.1016/j.dsp.2007.05.004. |
| [13] |
J. L. Liu, Y. Sun, J. Yang, W. Y. Liu and W. M. Chen,
Optimal sensor scheduling for hybrid estimation, Journal of Central South University, 20 (2013), 2186-2194.
doi: 10.1007/s11771-013-1723-4. |
| [14] |
B. M. Miller,
Observation control for discrete-continuous stochastic systems, IEEE Transactions on Automatic Control, 45 (2000), 993-998.
doi: 10.1109/9.855571. |
| [15] |
V. Malyavej, I. R. Manchester and A. V. Savkin,
Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints, Automatica, 42 (2006), 763-769.
doi: 10.1016/j.automatica.2005.12.024. |
| [16] |
A. S. Matveev and A. V. Savki,
Optimal state estimation in networked systems with asynchronous communication channels and switched sensors, Journal of optimization theory and applications, 128 (2006), 139-165.
doi: 10.1007/s10957-005-7562-1. |
| [17] |
A. V. Savkin, R. J. Evans and E. Skafidas,
The problem of optimal robust sensor scheduling, Systems Control Lett., 43 (2001), 149-157.
doi: 10.1016/S0167-6911(01)00086-X. |
| [18] |
S. L. Sun,
Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother, Automatica, 41 (2005), 2153-2159.
doi: 10.1016/j.automatica.2005.06.014. |
| [19] |
K. L. Teo, C. Goh and K. Wong,
A Unified Computational Approach to Optimal Control Problems, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
| [20] |
C. Z. Wu, K. L. Teo and X. Y. Wang,
Minimax optimal control of linear system with input-dependent uncertainty, Journal of the Franklin Institute, 351 (2014), 2742-2754.
doi: 10.1016/j.jfranklin.2014.01.012. |
| [21] |
C. Z. Wu, K. L. Teo and S. Y. Wu,
Min-max optimal control of linear systems with uncertainty and terminal state constraints, Automatica, 49 (2013), 1809-1815.
doi: 10.1016/j.automatica.2013.02.052. |
| [22] |
M. Yavuz and D. Jeffcoat, An analysis and solution of the sensor scheduling problem, In
Advances in Cooperative Control and Optimization, Springer Berlin Heidelberg, 369 (2007),
167–177.
doi: 10.1007/978-3-540-74356-9_10. |
show all references
References:
| [1] |
T. Abburi and S. Narasimhan,
Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory, IEEE Transactions on Automatic Control, 59 (2014), 2978-2983.
doi: 10.1109/TAC.2014.2351692. |
| [2] |
Z. L. Deng, Y. Gao, L. Mao, Y. Li and G. Hao,
New approach to information fusion steady-state Kalman filtering, Automatica, 41 (2005), 1695-1707.
doi: 10.1016/j.automatica.2005.04.020. |
| [3] |
Z. G. Feng, K. L. Teo and Y. Zhao,
Branch and bound method for sensor scheduling in discrete time, Journal of Industrial and Management Optimization, 1 (2005), 499-512.
doi: 10.3934/jimo.2005.1.499. |
| [4] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for Kalman filtering, Discrete and ContinuousDynamical Systems, 14 (2006), 483-503.
|
| [5] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for discrete Kalman filtering, Dynamic Systems and Applications, 16 (2007), 393-406.
|
| [6] |
Z. G. Feng, K. L. Teo and V. Rehbock,
Hybrid method for a general optimal sensor scheduling problem in discrete time, Automatica, 44 (2008), 1295-1303.
doi: 10.1016/j.automatica.2007.09.024. |
| [7] |
F. N. Grigor'ev and N. A. Kuznetsov,
Control of the observation process in continuous systems, Problems of Control and Information Theory, 6 (1977), 181-201.
|
| [8] |
F. N. Grigor'ev,
About the control of information processing in discrete automatic systems, Automation and Remote Control, 43 (1982).
|
| [9] |
H. Kushner,
On the optimum timing of observations for linear control systems with unknown initial state, IEEE Transactions on Automatic Control, 9 (1964), 144-150.
|
| [10] |
H. W. J. Lee, K. L. Teo and L. S. Jennings,
Control parametrization enhancing techniques for optimal discrete-valued control problems, Automatica, 35 (1999), 1401-1407.
doi: 10.1016/S0005-1098(99)00050-3. |
| [11] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim,
Sensor scheduling in continuous time, Automatica, 37 (2001), 2017-2023.
doi: 10.1016/S0005-1098(01)00159-5. |
| [12] |
Y. Li, L. W. Krakow, E. K. Chong and K. N. Groom,
Approximate stochastic dynamic programming for sensor scheduling to track multiple targets, Digital Signal Processing, 19 (2009), 978-989.
doi: 10.1016/j.dsp.2007.05.004. |
| [13] |
J. L. Liu, Y. Sun, J. Yang, W. Y. Liu and W. M. Chen,
Optimal sensor scheduling for hybrid estimation, Journal of Central South University, 20 (2013), 2186-2194.
doi: 10.1007/s11771-013-1723-4. |
| [14] |
B. M. Miller,
Observation control for discrete-continuous stochastic systems, IEEE Transactions on Automatic Control, 45 (2000), 993-998.
doi: 10.1109/9.855571. |
| [15] |
V. Malyavej, I. R. Manchester and A. V. Savkin,
Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints, Automatica, 42 (2006), 763-769.
doi: 10.1016/j.automatica.2005.12.024. |
| [16] |
A. S. Matveev and A. V. Savki,
Optimal state estimation in networked systems with asynchronous communication channels and switched sensors, Journal of optimization theory and applications, 128 (2006), 139-165.
doi: 10.1007/s10957-005-7562-1. |
| [17] |
A. V. Savkin, R. J. Evans and E. Skafidas,
The problem of optimal robust sensor scheduling, Systems Control Lett., 43 (2001), 149-157.
doi: 10.1016/S0167-6911(01)00086-X. |
| [18] |
S. L. Sun,
Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother, Automatica, 41 (2005), 2153-2159.
doi: 10.1016/j.automatica.2005.06.014. |
| [19] |
K. L. Teo, C. Goh and K. Wong,
A Unified Computational Approach to Optimal Control Problems, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
| [20] |
C. Z. Wu, K. L. Teo and X. Y. Wang,
Minimax optimal control of linear system with input-dependent uncertainty, Journal of the Franklin Institute, 351 (2014), 2742-2754.
doi: 10.1016/j.jfranklin.2014.01.012. |
| [21] |
C. Z. Wu, K. L. Teo and S. Y. Wu,
Min-max optimal control of linear systems with uncertainty and terminal state constraints, Automatica, 49 (2013), 1809-1815.
doi: 10.1016/j.automatica.2013.02.052. |
| [22] |
M. Yavuz and D. Jeffcoat, An analysis and solution of the sensor scheduling problem, In
Advances in Cooperative Control and Optimization, Springer Berlin Heidelberg, 369 (2007),
167–177.
doi: 10.1007/978-3-540-74356-9_10. |
Figure 2.
he cost function values in the first example
Figure 3.
Optimal solutions of the second example
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